Question 5
Find all functions $f:\mathbb R\to\mathbb R$ such that, for all real $x,y$,
$$f(x^2-y)+2yf(x)=f(f(x))+f(y).$$
Proposed by Carl Schildkraut. Source: Evan Chen’s third-party compilation; https://aops.com/community/p30227204. One editorial point; manual grading.
$$f(x^2-y)+2yf(x)=f(f(x))+f(y).$$
Proposed by Carl Schildkraut. Source: Evan Chen’s third-party compilation; https://aops.com/community/p30227204. One editorial point; manual grading.